American Institute of Mathematical Sciences

Advanced
doi: 10.3934/jimo.2020165

Coordination of a sustainable reverse supply chain with revenue sharing contract

Sushil Kumar Dey and  Bibhas C. Giri ,

Department of Mathematics, Jadavpur University, Kolkata-700032, India

* Corresponding author: Bibhas C. Giri

Received  February 2020 Revised  August 2020 Published  November 2020

In this article, a three-echelon closed-loop supply chain is considered under sustainability consideration through remanufacturing of waste materials. Depending upon quality, the collector collects the used products and forwards to the manufacturer for remanufacturing. The collector offers a reward or incentive to consumers to influence them to return the used items. The shortfall amount of collected used items, if any, is meet up by the supplier by supplying fresh raw materials. In three separate cases viz centralized, decentralized and revenue-sharing contract, optimal incentives for end-customers and optimal profits of supply chain members are determined. The revenue-sharing contract is implemented in two different settings - one including the supplier and the other one excluding the supplier. The win-win outcome for the supply chain members is investigated and a specific range of the sharing parameter for win-win outcome is obtained. Optimal results are supported by numerical analysis, and sensitivity of the optimal results with respect to key parameters is analyzed.

Keywords: Supply chain, recycling, quality uncertainty, revenue sharing contract.
Mathematics Subject Classification: Primary: 90B06; Secondary: 91A35.
Citation: Sushil Kumar Dey, Bibhas C. Giri. Coordination of a sustainable reverse supply chain with revenue sharing contract. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020165
References:
[1]

B. Ageron, A. Gunasekaran and A. Spalanzani, Sustainable supply management: An empirical study, International Journal of Production Economics, 140 (2012), 168-182.  doi: 10.1016/j.ijpe.2011.04.007.  Google Scholar

[2]

L. Aramyan, R. Hoste, W. Van Den Broek, J. Groot, H. Soethoudt, T. L. Nguyen, J. Hermansen and J. van der Vorst, Towards sustainable food production: A scenario study of the European pork sector, Journal on Chain and Network Science, 11 (2011), 177-189.  doi: 10.3920/JCNS2011.Qpork8.  Google Scholar

[3]

A. N. Arnette, B. L. Brewer and T. Choal, Design for sustainability (DFS): The intersection of supply chain and environment, Journal of Cleaner Production, 83 (2004), 374-390.  doi: 10.1016/j.jclepro.2014.07.021.  Google Scholar

[4]

Q. Bai, M. Chen and L. Xu, Revenue and promotional cost-sharing contract versus two-part tariff contract in coordinating sustainable supply chain systems with deteriorating items, International Journal of Production Economics, 187 (2017), 85-101.   Google Scholar

[5]

Z. Basiri and J. Heydari, A mathematical model for green supply chain coordination with sustainable products, Journal of Cleaner Production, 145 (2017), 232-249.   Google Scholar

[6]

Y. Bouchery, A. Ghaffari, Z. Jemai and J. Fransoo, Sustainable transportation and order quantity: Insights from multi-objective optimization, Flexible Services and Manufacturing Journal, 28 (2016), 367-396.   Google Scholar

[7]

G. P. Cachon, Supply chain coordination with contracts, Handbooks in Operations Research and Management Science, 11 (2003), 227-339.  doi: 10.1016/S0927-0507(03)11006-7.  Google Scholar

[8]

O. Capraz, O. Polat and A. Gungor, Planning of waste electrical and electronic equipment(WEEE) recycling facilities: MILP modelling and case study investigation, Flexible Services and Manufacturing Journal, 27 (2015), 479-508.  doi: 10.1007/s10696-015-9217-3.  Google Scholar

[9]

X. Chen, H. Zhang, M. Zhang and J. Chen, Optimal decisions in a retailer Stackelberg supply chain, International Journal of Production Economics, 187 (2017), 260-270.  doi: 10.1016/j.ijpe.2017.03.002.  Google Scholar

[10]

B. Chen, W. Xie, F. Huang and J. He, Quality competition and coordination in a VMI supply chain with two risk-averse manufacturers, Journal of Industrial and Management Optimization, http://dx.doi.org/10.3934/jimo.2020100. Google Scholar

[11]

D. Chen, J. Ignatis, D. Sun, S. Zhan, C. Zhou, M. Marra and M. Demirbag, Reverse logistics pricing strategy for a green supply chain: A view of customer's environmental awareness, International Journal of Production Economics, 217 (2019), 197-210.  doi: 10.1016/j.ijpe.2018.08.031.  Google Scholar

[12]

K. Das and AH. Chowdhury, Designing a reverse logistics network for optimal collection, recovery and quality-based product-mix planning, International Journal of Production Economics, 135 (2012), 209-221.  doi: 10.1016/j.ijpe.2011.07.010.  Google Scholar

[13]

M. Eskandarpour, P. Dejax, J. Miemczyk and O. Péton, Sustainable supply chain network design: An optimization-oriented review, Omega, 54 (2015), 11-32.   Google Scholar

[14]

B. C. Giri and B. R. Sarker, Coordinating a multi-echelon supply chain under production disruption and price-sensitive stochastic demand, Journal of Industrial and Management Optimization, 15 (2019), 1631-1651.  doi: 10.3934/jimo.2018115.  Google Scholar

[15]

B. C. Giri and S. K. Dey, Game theoretic analysis of a closed-loop supply chain with backup supplier under dual channel recycling, Computers and Industrial Engineering, 129 (2019), 179-191.  doi: 10.1016/j.cie.2019.01.035.  Google Scholar

[16]

K. Govindan, S. G. Azevedo, H. Carvalho and V. Cruz-Machado, Impact of Supply chain Management practices on sustainability, Journal of Cleaner Production, 85 (2014), 212-225.  doi: 10.1016/j.jclepro.2014.05.068.  Google Scholar

[17]

K. Govindan and M. N. Popiuc, Reverse supply chain coordination by revenue sharing contract: A case for the personal computers industry, European Journal of Operational Research, 233 (2014), 326-336.  doi: 10.1016/j.ejor.2013.03.023.  Google Scholar

[18]

K. W. Green, P. J. Zelbst, J. Meacham and V. S. Bhadauria, Green supply chain management practices: Impact on performance, Supply Chain Management: An International Journal, 17 (2012), 290-305.  doi: 10.1108/13598541211227126.  Google Scholar

[19]

J. Heydari, K. Govindan and A. Jafari, Reverse and closed loop supply chain coordination by considering government role, Transportation Research Part D: Transport and Environment, 52 (2017), 379-398.  doi: 10.1016/j.trd.2017.03.008.  Google Scholar

[20]

J. Heydari and M. Ghasemi, A revenue sharing contract for reverse supply chain coordination under stochastic quality of returned products and uncertain remanufacturing capacity, Journal of Cleaner Production, 197 (2018), 607-615.  doi: 10.1016/j.jclepro.2018.06.206.  Google Scholar

[21]

J. Heydari, K. Govindan and R. Sadeghi, Reverse supply chain coordination under stochastic remanufacturing capacity, International Journal of Production Economics, 202 (2018), 1-11.  doi: 10.1016/j.ijpe.2018.04.024.  Google Scholar

[22]

S. Hu, Y. Dai, Z. J. Ma and Y. S. Ye, Designing contracts for a reverse supply chainwith strategic recycling behavior of consumers, International Journal of Production Economics, 180 (2016), 16-24.   Google Scholar

[23]

B. Hu and Y. Feng, Optimization and coordination of supply chain with revenue sharing contracts and service requirement under supply and demand uncertainty, International Journal of Production Economics, 183 (2017), 185-193.   Google Scholar

[24]

G. Hua, S. Wang and T. C. E. Cheng, Price and lead time decisions in dual-channel supply chains, European Journal of Operational Research, 205 (2010), 113-126.  doi: 10.1016/j.ejor.2009.12.012.  Google Scholar

[25]

F. Huang, J. He and J. Wang, Coordination of VMI supply chain with a loss-averse manufacturer under quality-dependency and marketing-dependency, Journal of Industrial and Management Optimization, 15 (2019), 1753-1772.  doi: 10.3934/jimo.2018121.  Google Scholar

[26]

F. Huang, J. He and Q. Lai, Coordination in a retailer-dominated supply chain with a risk-averse manufacturer under marketing dependency, International Transactions in Operational Research, 27 (2020), 3056-3078.  doi: 10.1111/itor.12520.  Google Scholar

[27]

H. Jafari, S. R. Hejazi and R. B. Morteza, Sustainable development by waste recycling under a three-echelon supply chain: A game-theoretic approach, Journal of Cleaner Production, 142 (2017), 2252-2261.   Google Scholar

[28]

H. S. Kilic, U. Cebeci and M. B. Ayhan, Reverse logistics system design for the waste of electrical and electronic equipment (WEEE) in Turkey, Resource Conservation and Recycling, 95 (2015), 120-132.  doi: 10.1016/j.resconrec.2014.12.010.  Google Scholar

[29]

K. Kim, B. Jeong and H. Jung, Supply chain surplus: Comparing conventional and sustainable supply chains, Flexible Services and Manufacturing Journal, 26 (2014), 5-23.  doi: 10.1007/s10696-012-9163-2.  Google Scholar

[30]

S. Kushwaha, A. Ghosh and A. K. Rao, Collection activity channels selection in a reverse supply chain a carbon cap-and-trade regulation, Journal of Cleaner Production, 260 (2020), 121034. doi: 10.1016/j.jclepro.2020.121034.  Google Scholar

[31]

Y. Li, F. Xu and X. Zhao, Governance mechanisms of dual-channel reverse supply chains with informal collection channel, Journal of Cleaner Production, 155 (2017), 125-140.  doi: 10.1016/j.jclepro.2016.09.084.  Google Scholar

[32]

T. Li, R. Zhang, S. Zhao and B. Liu, Low carbon strategy analysis under revenue-sharing and cost-sharing contracts, Journal of Cleaner Production, 212 (2019), 1462-1477.  doi: 10.1016/j.jclepro.2018.11.282.  Google Scholar

[33]

L. Liu, Z. Wang, L. Xu, X. Hong and K. Govindan, Collection effort and reverse channel choices in a closed-loop supply chain, Journal of Cleaner Production, 144 (2017), 492-500.  doi: 10.1016/j.jclepro.2016.12.126.  Google Scholar

[34]

C. L. Martins and M. V. Pato, Supply chain sustainability: A tertiary literature review, Journal of Cleaner Production, 225 (2019), 995-1016.  doi: 10.1016/j.jclepro.2019.03.250.  Google Scholar

[35]

M. Reimann, Y. Xiong and Y. Zhou, Managing a closed-loop supply chain with process innovation for remanufacturing, European Journal of Operational Research, 276 (2019), 510-518.  doi: 10.1016/j.ejor.2019.01.028.  Google Scholar

[36]

P. Rogetzer, L. Silbermayr and W. Jammernegg, Sustainable sourcing of strategic raw materials by integrating recycled materials, Flexible Services and Manufacturing Journal, 30 (2018), 421-451.  doi: 10.1007/s10696-017-9288-4.  Google Scholar

[37]

R. Sadeghi, A. A. Taleizadeh, F. T. S. Chen and J. Heydari, Coordinating and pricing decisions in two competitive reverse supply chains with different channel structures, International Journal of Production Research, 57 (2019), 2601-2625.  doi: 10.1080/00207543.2018.1551637.  Google Scholar

[38]

S. Saha, S. P. Sarmah and I. Moon, Dual channel closed-loop supply chain coordination with a reward-driven remanufacturing policy, International Journal of Production Research, 54 (2016), 1503-1517.  doi: 10.1080/00207543.2015.1090031.  Google Scholar

[39]

H. Song and X. Gao, Green supply chain game model and analysis under revenue-sharing contract, Journal of Cleaner Production, 170 (2018), 183-192.  doi: 10.1016/j.jclepro.2017.09.138.  Google Scholar

[40]

A. A. Taleizadeh and R. Sadeghi, Pricing strategies in the competitive reverse supply chains with traditional and e-channels: A game theoretic approach, International Journal of Production Economics, 215 (2019), 48-60.  doi: 10.1016/j.ijpe.2018.06.011.  Google Scholar

[41]

W. Wang, P. Zhang, J. Ding, J. Li, H. Sun and L. He, Closed-loop supply chain network equilibrium model with retailer-collection under legislation, Journal of Industrial and Management Optimization, 15 (2019), 199-219.  doi: 10.3934/jimo.2018039.  Google Scholar

[42]

D. Weraikat, M. K. Zanjani and N. Lehoux, Two-echelon pharmaceutical reverse supply chain coordination with customers incentives, International Journal of Production Economics, 176 (2016), 41-52.  doi: 10.1016/j.ijpe.2016.03.003.  Google Scholar

[43]

W. Xie, B. Chen, F. Huang and J. He, Coordination of a Supply Chain with a Loss-averse retailer under supply uncertainty and marketing effort, Journal of Industrial and Management Optimization, http://dx.doi.org/10.3934/jimo.2020125. Google Scholar

[44]

A. Z. Zeng, Coordination mechanisms for a three-stage reverse supply chain to increase profitable returns, Naval Research Logistics, 60 (2012), 31-45.  doi: 10.1002/nav.21517.  Google Scholar

[45]

A. Z. Zeng and J. Hou, Procurement and coordination under imperfect quality and uncertain demand in reverse mobile phone supply chain, International Journal of Production Economics, 209 (2019), 346-359.   Google Scholar

[46]

B. Zheng, C. Yang, J. Yang and M. Zhang, Pricing, collecting and contract design in a reverse supply chain with incomplete information, Computers and Industrial Engineering, 111 (2017), 109-122.  doi: 10.1016/j.cie.2017.07.004.  Google Scholar

show all references

References:
[1]

B. Ageron, A. Gunasekaran and A. Spalanzani, Sustainable supply management: An empirical study, International Journal of Production Economics, 140 (2012), 168-182.  doi: 10.1016/j.ijpe.2011.04.007.  Google Scholar

[2]

L. Aramyan, R. Hoste, W. Van Den Broek, J. Groot, H. Soethoudt, T. L. Nguyen, J. Hermansen and J. van der Vorst, Towards sustainable food production: A scenario study of the European pork sector, Journal on Chain and Network Science, 11 (2011), 177-189.  doi: 10.3920/JCNS2011.Qpork8.  Google Scholar

[3]

A. N. Arnette, B. L. Brewer and T. Choal, Design for sustainability (DFS): The intersection of supply chain and environment, Journal of Cleaner Production, 83 (2004), 374-390.  doi: 10.1016/j.jclepro.2014.07.021.  Google Scholar

[4]

Q. Bai, M. Chen and L. Xu, Revenue and promotional cost-sharing contract versus two-part tariff contract in coordinating sustainable supply chain systems with deteriorating items, International Journal of Production Economics, 187 (2017), 85-101.   Google Scholar

[5]

Z. Basiri and J. Heydari, A mathematical model for green supply chain coordination with sustainable products, Journal of Cleaner Production, 145 (2017), 232-249.   Google Scholar

[6]

Y. Bouchery, A. Ghaffari, Z. Jemai and J. Fransoo, Sustainable transportation and order quantity: Insights from multi-objective optimization, Flexible Services and Manufacturing Journal, 28 (2016), 367-396.   Google Scholar

[7]

G. P. Cachon, Supply chain coordination with contracts, Handbooks in Operations Research and Management Science, 11 (2003), 227-339.  doi: 10.1016/S0927-0507(03)11006-7.  Google Scholar

[8]

O. Capraz, O. Polat and A. Gungor, Planning of waste electrical and electronic equipment(WEEE) recycling facilities: MILP modelling and case study investigation, Flexible Services and Manufacturing Journal, 27 (2015), 479-508.  doi: 10.1007/s10696-015-9217-3.  Google Scholar

[9]

X. Chen, H. Zhang, M. Zhang and J. Chen, Optimal decisions in a retailer Stackelberg supply chain, International Journal of Production Economics, 187 (2017), 260-270.  doi: 10.1016/j.ijpe.2017.03.002.  Google Scholar

[10]

B. Chen, W. Xie, F. Huang and J. He, Quality competition and coordination in a VMI supply chain with two risk-averse manufacturers, Journal of Industrial and Management Optimization, http://dx.doi.org/10.3934/jimo.2020100. Google Scholar

[11]

D. Chen, J. Ignatis, D. Sun, S. Zhan, C. Zhou, M. Marra and M. Demirbag, Reverse logistics pricing strategy for a green supply chain: A view of customer's environmental awareness, International Journal of Production Economics, 217 (2019), 197-210.  doi: 10.1016/j.ijpe.2018.08.031.  Google Scholar

[12]

K. Das and AH. Chowdhury, Designing a reverse logistics network for optimal collection, recovery and quality-based product-mix planning, International Journal of Production Economics, 135 (2012), 209-221.  doi: 10.1016/j.ijpe.2011.07.010.  Google Scholar

[13]

M. Eskandarpour, P. Dejax, J. Miemczyk and O. Péton, Sustainable supply chain network design: An optimization-oriented review, Omega, 54 (2015), 11-32.   Google Scholar

[14]

B. C. Giri and B. R. Sarker, Coordinating a multi-echelon supply chain under production disruption and price-sensitive stochastic demand, Journal of Industrial and Management Optimization, 15 (2019), 1631-1651.  doi: 10.3934/jimo.2018115.  Google Scholar

[15]

B. C. Giri and S. K. Dey, Game theoretic analysis of a closed-loop supply chain with backup supplier under dual channel recycling, Computers and Industrial Engineering, 129 (2019), 179-191.  doi: 10.1016/j.cie.2019.01.035.  Google Scholar

[16]

K. Govindan, S. G. Azevedo, H. Carvalho and V. Cruz-Machado, Impact of Supply chain Management practices on sustainability, Journal of Cleaner Production, 85 (2014), 212-225.  doi: 10.1016/j.jclepro.2014.05.068.  Google Scholar

[17]

K. Govindan and M. N. Popiuc, Reverse supply chain coordination by revenue sharing contract: A case for the personal computers industry, European Journal of Operational Research, 233 (2014), 326-336.  doi: 10.1016/j.ejor.2013.03.023.  Google Scholar

[18]

K. W. Green, P. J. Zelbst, J. Meacham and V. S. Bhadauria, Green supply chain management practices: Impact on performance, Supply Chain Management: An International Journal, 17 (2012), 290-305.  doi: 10.1108/13598541211227126.  Google Scholar

[19]

J. Heydari, K. Govindan and A. Jafari, Reverse and closed loop supply chain coordination by considering government role, Transportation Research Part D: Transport and Environment, 52 (2017), 379-398.  doi: 10.1016/j.trd.2017.03.008.  Google Scholar

[20]

J. Heydari and M. Ghasemi, A revenue sharing contract for reverse supply chain coordination under stochastic quality of returned products and uncertain remanufacturing capacity, Journal of Cleaner Production, 197 (2018), 607-615.  doi: 10.1016/j.jclepro.2018.06.206.  Google Scholar

[21]

J. Heydari, K. Govindan and R. Sadeghi, Reverse supply chain coordination under stochastic remanufacturing capacity, International Journal of Production Economics, 202 (2018), 1-11.  doi: 10.1016/j.ijpe.2018.04.024.  Google Scholar

[22]

S. Hu, Y. Dai, Z. J. Ma and Y. S. Ye, Designing contracts for a reverse supply chainwith strategic recycling behavior of consumers, International Journal of Production Economics, 180 (2016), 16-24.   Google Scholar

[23]

B. Hu and Y. Feng, Optimization and coordination of supply chain with revenue sharing contracts and service requirement under supply and demand uncertainty, International Journal of Production Economics, 183 (2017), 185-193.   Google Scholar

[24]

G. Hua, S. Wang and T. C. E. Cheng, Price and lead time decisions in dual-channel supply chains, European Journal of Operational Research, 205 (2010), 113-126.  doi: 10.1016/j.ejor.2009.12.012.  Google Scholar

[25]

F. Huang, J. He and J. Wang, Coordination of VMI supply chain with a loss-averse manufacturer under quality-dependency and marketing-dependency, Journal of Industrial and Management Optimization, 15 (2019), 1753-1772.  doi: 10.3934/jimo.2018121.  Google Scholar

[26]

F. Huang, J. He and Q. Lai, Coordination in a retailer-dominated supply chain with a risk-averse manufacturer under marketing dependency, International Transactions in Operational Research, 27 (2020), 3056-3078.  doi: 10.1111/itor.12520.  Google Scholar

[27]

H. Jafari, S. R. Hejazi and R. B. Morteza, Sustainable development by waste recycling under a three-echelon supply chain: A game-theoretic approach, Journal of Cleaner Production, 142 (2017), 2252-2261.   Google Scholar

[28]

H. S. Kilic, U. Cebeci and M. B. Ayhan, Reverse logistics system design for the waste of electrical and electronic equipment (WEEE) in Turkey, Resource Conservation and Recycling, 95 (2015), 120-132.  doi: 10.1016/j.resconrec.2014.12.010.  Google Scholar

[29]

K. Kim, B. Jeong and H. Jung, Supply chain surplus: Comparing conventional and sustainable supply chains, Flexible Services and Manufacturing Journal, 26 (2014), 5-23.  doi: 10.1007/s10696-012-9163-2.  Google Scholar

[30]

S. Kushwaha, A. Ghosh and A. K. Rao, Collection activity channels selection in a reverse supply chain a carbon cap-and-trade regulation, Journal of Cleaner Production, 260 (2020), 121034. doi: 10.1016/j.jclepro.2020.121034.  Google Scholar

[31]

Y. Li, F. Xu and X. Zhao, Governance mechanisms of dual-channel reverse supply chains with informal collection channel, Journal of Cleaner Production, 155 (2017), 125-140.  doi: 10.1016/j.jclepro.2016.09.084.  Google Scholar

[32]

T. Li, R. Zhang, S. Zhao and B. Liu, Low carbon strategy analysis under revenue-sharing and cost-sharing contracts, Journal of Cleaner Production, 212 (2019), 1462-1477.  doi: 10.1016/j.jclepro.2018.11.282.  Google Scholar

[33]

L. Liu, Z. Wang, L. Xu, X. Hong and K. Govindan, Collection effort and reverse channel choices in a closed-loop supply chain, Journal of Cleaner Production, 144 (2017), 492-500.  doi: 10.1016/j.jclepro.2016.12.126.  Google Scholar

[34]

C. L. Martins and M. V. Pato, Supply chain sustainability: A tertiary literature review, Journal of Cleaner Production, 225 (2019), 995-1016.  doi: 10.1016/j.jclepro.2019.03.250.  Google Scholar

[35]

M. Reimann, Y. Xiong and Y. Zhou, Managing a closed-loop supply chain with process innovation for remanufacturing, European Journal of Operational Research, 276 (2019), 510-518.  doi: 10.1016/j.ejor.2019.01.028.  Google Scholar

[36]

P. Rogetzer, L. Silbermayr and W. Jammernegg, Sustainable sourcing of strategic raw materials by integrating recycled materials, Flexible Services and Manufacturing Journal, 30 (2018), 421-451.  doi: 10.1007/s10696-017-9288-4.  Google Scholar

[37]

R. Sadeghi, A. A. Taleizadeh, F. T. S. Chen and J. Heydari, Coordinating and pricing decisions in two competitive reverse supply chains with different channel structures, International Journal of Production Research, 57 (2019), 2601-2625.  doi: 10.1080/00207543.2018.1551637.  Google Scholar

[38]

S. Saha, S. P. Sarmah and I. Moon, Dual channel closed-loop supply chain coordination with a reward-driven remanufacturing policy, International Journal of Production Research, 54 (2016), 1503-1517.  doi: 10.1080/00207543.2015.1090031.  Google Scholar

[39]

H. Song and X. Gao, Green supply chain game model and analysis under revenue-sharing contract, Journal of Cleaner Production, 170 (2018), 183-192.  doi: 10.1016/j.jclepro.2017.09.138.  Google Scholar

[40]

A. A. Taleizadeh and R. Sadeghi, Pricing strategies in the competitive reverse supply chains with traditional and e-channels: A game theoretic approach, International Journal of Production Economics, 215 (2019), 48-60.  doi: 10.1016/j.ijpe.2018.06.011.  Google Scholar

[41]

W. Wang, P. Zhang, J. Ding, J. Li, H. Sun and L. He, Closed-loop supply chain network equilibrium model with retailer-collection under legislation, Journal of Industrial and Management Optimization, 15 (2019), 199-219.  doi: 10.3934/jimo.2018039.  Google Scholar

[42]

D. Weraikat, M. K. Zanjani and N. Lehoux, Two-echelon pharmaceutical reverse supply chain coordination with customers incentives, International Journal of Production Economics, 176 (2016), 41-52.  doi: 10.1016/j.ijpe.2016.03.003.  Google Scholar

[43]

W. Xie, B. Chen, F. Huang and J. He, Coordination of a Supply Chain with a Loss-averse retailer under supply uncertainty and marketing effort, Journal of Industrial and Management Optimization, http://dx.doi.org/10.3934/jimo.2020125. Google Scholar

[44]

A. Z. Zeng, Coordination mechanisms for a three-stage reverse supply chain to increase profitable returns, Naval Research Logistics, 60 (2012), 31-45.  doi: 10.1002/nav.21517.  Google Scholar

[45]

A. Z. Zeng and J. Hou, Procurement and coordination under imperfect quality and uncertain demand in reverse mobile phone supply chain, International Journal of Production Economics, 209 (2019), 346-359.   Google Scholar

[46]

B. Zheng, C. Yang, J. Yang and M. Zhang, Pricing, collecting and contract design in a reverse supply chain with incomplete information, Computers and Industrial Engineering, 111 (2017), 109-122.  doi: 10.1016/j.cie.2017.07.004.  Google Scholar

Figure 1.  Diagram of the supply chain model
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Figure 2.  Proposed supply chain model under revenue sharing contract
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Figure 3.  Concavity of $ E(\Pi) $ w.r.to $ p $ and $ r $
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Figure 4.  $ L $ vs. profits of the SC and its entities
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Figure 5.  $ b $ vs. profits of the SC and its entities
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Figure 6.  $ r^{max} $ vs. profits of the SC and its entities
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Table 1.  Optimal results
Model $ r^{*} $ $ p^{*} $ $ 1-\phi $ $ \phi_{1}+\phi_{2} $ $ E(\Pi_{c}) $ $ E(\Pi_{m}) $ $ E(\Pi_{s}) $ $ E(\Pi) $
Centralized 26.67 437 - - - - - 143535
Decentralized 46.67 463 - - 6505 122018 10355 138878
RS-I 26.67 437 .01 - 7662 125518 10355 143535
RS-II 26.67 437 - 0.03 - 124536 - 143535
Table Options

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Model $ r^{*} $ $ p^{*} $ $ 1-\phi $ $ \phi_{1}+\phi_{2} $ $ E(\Pi_{c}) $ $ E(\Pi_{m}) $ $ E(\Pi_{s}) $ $ E(\Pi) $
Centralized 26.67 437 - - - - - 143535
Decentralized 46.67 463 - - 6505 122018 10355 138878
RS-I 26.67 437 .01 - 7662 125518 10355 143535
RS-II 26.67 437 - 0.03 - 124536 - 143535
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